{
  "id": "1105.5633",
  "version": "v2",
  "published": "2011-05-27T19:16:00.000Z",
  "updated": "2011-10-27T19:33:54.000Z",
  "title": "Algebraic divisibility sequences over function fields",
  "authors": [
    "Patrick Ingram",
    "Valéry Mahé",
    "Joseph H. Silverman",
    "Katherine E. Stange",
    "Marco Streng"
  ],
  "comment": "28 pages",
  "journal": "J. Australian Math. Soc. 92 (2012), 99-126",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We study the existence of primes and of primitive divisors in classical divisibility sequences defined over function fields. Under various hypotheses, we prove that Lucas sequences and elliptic divisibility sequences over function fields defined over number fields contain infinitely many irreducible elements. We also prove that an elliptic divisibility sequence over a function field has only finitely many terms lacking a primitive divisor.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-10-27T19:33:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B39",
      "11G05"
    ],
    "keywords": [
      "function field",
      "algebraic divisibility sequences",
      "elliptic divisibility sequence",
      "primitive divisor",
      "number fields contain"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.5633I"
    }
  }
}